Problem: Express your answer as a mixed number simplified to lowest terms. $17\dfrac{4}{9}-12\dfrac{2}{3} = {?}$
Explanation: Find a common denominator for the fractions: $= {17\dfrac{4}{9}}-{12\dfrac{6}{9}}$ Convert ${17\dfrac{4}{9}}$ to ${16 + \dfrac{9}{9} + \dfrac{4}{9}}$ So the problem becomes: ${16\dfrac{13}{9}}-{12\dfrac{6}{9}}$ Separate the whole numbers from the fractional parts: $= {16} + {\dfrac{13}{9}} - {12} - {\dfrac{6}{9}}$ Bring the whole numbers together and the fractions together: $= {16} - {12} + {\dfrac{13}{9}} - {\dfrac{6}{9}}$ Subtract the whole numbers: $=4 + {\dfrac{13}{9}} - {\dfrac{6}{9}}$ Subtract the fractions: $= 4+\dfrac{7}{9}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{7}{9}$